Question

PLEASE HELP ME PLEASE AND THANK

Answer 1

Answer: OPTION C.

Explanation:

You can observe in the picture given in the exercise that
`\angle E` is formed by two secants intersecting outside the circle.

It is necessary to remember that, by definition:

`Angle\ formed\ by\ two\ Secants=(1)/(2)(Difference\ of\ Intercepted\ Arcs)`

You can also identify that the Intercepted Arcs are the following:

`CD=110\°\\\\AB=30\°`

Then, knowing the measures of the Intercepted Arcs, you can substitute them into the equation shown before and then evaluate, in order to calculate the measure of
`\angle E` , which is the angle formed by the intersection of the secants.

Therefore, you get:

`m\angle E=(1)/(2)(110\°-30\°)\\\\m\angle E=40\°`